Electronic Supplementary Information to A Cu-Zn-Cu-Zn heterometallomacrocycle shows significant antiferromagnetic coupling between paramagnetic centres mediated by diamagnetic metal Elena A. Buvaylo, a Vladimir N. Kokozay, a Olga Yu. Vassilyeva, a Brian W. Skelton, b Julia Jezierska, c Louis C. Brunel d and Andrew Ozarowski* d a Department of Inorganic Chemistry, National Taras Shevchenko University, Volodimirska str. 64, Kyiv 01033, Ukraine b Chemistry, School of Biomedical and Chemical Sciences, University of Western Australia, Crawley, Western Australia 6009 c Faculty of Chemistry, University of Wroclaw, 14 Joliot-Curie Str., 50-383 Wroclaw, Poland d National High Magnetic Field Laboratory, FSU 1800 E. Paul Dirac Dr., Tallahassee, FL 32310-3706, USA, Fax: 850-644-1366; Tel: 850-644-5996; E-mail: ozarowsk@magnet.fsu.edu
30 K Magnetic Induction, Tesla 12.0 12.2 12.4 12.6 12.8 13.0 13.2 The 30 K spectrum of 1 at 377.24 GHz Blue: experimental, Red: spin-doublet spectrum simulated with the following parameters: g x = 2.0525 g y = 2.0546 g z = 2.2510 Anisotropic line shape, 50% Gaussian 50% Lorentzian, with the widths x=30 G, y=25 G, z=80 G. Linewidth is defined here for the derivative line as the distance from the zero-point to the peak. The spectrum can be simulated as coming from an S=1/2 state because the fine structure is lost due to the intermolecular interactions.
10 K Magnetic Induction, Tesla 2.95 3.00 3.05 3.10 3.15 3.20 3.25 The 10 K spectrum of 1 at 92.7675 GHz Blue: experimental, Red and Green: spin-triplet spectra simulated with the following parameters: Green: g x = 2.0527 g y = 2.0550 g z = 2.2507 D = -108 Gauss, E = 6 Gauss Red: g x = 2.0527 g y = 2.0550 g z = 2.2507 D = 108 Gauss, E = -6 Gauss To convert D, E from Gauss to cm -1 multiply by 4.6686 10-5 2.0023 For both simulated spectra: Z axis of the zero-field splitting tensor parallel to g x A x = A y = 0, A z = 80 Gauss, A z parallel to g z To convert A i from Gauss to cm -1 multiply by 4.6686 10-5 g i Isotropic line 40% Gaussian 60% Lorentzian, 20 Gauss width
10 K Magnetic Induction, Tesla 11.16 11.17 11.18 11.19 11.20 11.21 11.22 The perpendicular region of the 10 K spectrum of 1 at 321.600 GHz Blue: experimental, Red and Green: spin-triplet spectra simulated with the following parameters: Red: g x = 2.0529 g y = 2.0548 g z = 2.2507 D = 108 Gauss, E = -6 Gauss Green: g x = 2.0529 g y = 2.0548 g z = 2.2507 D = -108 Gauss, E = 6 Gauss To convert D, E from Gauss to cm -1 multiply by 4.6686 10-5 2.0023 For both simulated spectra: Z axis of the zero-field splitting tensor parallel to g x A x = A y = 0, A z = 80 Gauss, A z parallel to g z To convert A i from Gauss to cm -1 multiply by 4.6686 10-5 g i Isotropic line shape 40% Gaussian 60% Lorentzian, 20 Gauss width
10 K Magnetic Induction, Tesla 0.26 0.28 0.30 0.32 0.34 0.36 X-Band (9.391 GHz) spectrum of 1 at 10 K.
3.0 K Magnetic Induction, Tesla 2.90 2.95 3.00 3.05 3.10 3.15 3.20 3.25 The 3.0 K spectrum of 1 at 92.767 GHz Blue: experimental, Red: spin-doublet spectrum simulated with the following parameters: g x = 2.0512 g y = 2.0548 g z = 2.2480 A x =0, A y =0, A z =176 Gauss Anisotropic line width 50% Gaussian 50% Lorentzian, x=20 G, y=20 G, z=30 G
Magnetic susceptibility per ½ of the molar mass of 1 Temperature, K 10 6 χ, cgs emu 4.50 1019 5.00 945 5.50 889 6.00 861 7.00 869 8.00 990 9.00 1211 10.00 1522 12.00 2399 14.00 3312 16.00 4186 18.00 4936 20.00 5529 25.00 6392 30.00 6647 35.00 6564 40.00 6347 45.00 6074 50.00 5780 55.00 5492 60.00 5212 64.99 4951 70.00 4711 74.99 4489 79.99 4285 84.99 4098 89.99 3920 94.99 3763 100.00 3615 109.99 3348 119.99 3117 129.99 2917 139.99 2739 149.99 2580 159.98 2440 169.98 2316 179.98 2205 189.98 2103 199.98 2011 209.98 1928
219.98 1847 229.98 1777 239.98 1712 249.97 1651 259.98 1594 269.99 1541 279.99 1491 289.99 1444 299.99 1401 Note: To convert the molar susceptibility from cgs emu to SI units multiply the molar cgs emu value by 4π 10-6
Contribution of the dipole-dipole and exchange interaction to the Zero-Field splitting The relations between components of the diagonalized zero-field splitting tensor D and the D and E parameters of the Spin Hamiltonian are D = ( 2D zz - D xx - D yy ) / 2, E = ( D xx - D yy ) / 2 (1) The magnetic dipole-dipole interaction and the anisotropy of the exchange interactions contribute to the D tensor components: D = D dip + D ex (2) (Symbols in boldface represent tensors). The molecule of 1 is centrosymmetric and the formula for the components of the dipolar interaction tensor D dip given in ref. 11 simplifies to 2 3 ( Ddip ) kl = gk gl ( δkl 3σ kσ l ) µ B / 2r (3) where δ kl is the Kronecker s delta, σ k are cosines of the angles formed by the directions of the g components with the vector r joining the copper atoms. Tensor D dip is not necessarily traceless. To model the electron delocalization, the electron fractions ρ i, ρ j are placed at a series of points numbered by i for one copper ion and by j for another copper ion and the contributions from each pair i,j are summed up: 2 ( D ) = g g ( δ 3σ σ ) ρ ρ µ / 2r dip kl i j k l kl k l i j B 3 ij (4) r ij now represents the distance from point i to point j and σ k are the cosines of the angles formed by the directions of the g components with the vector r ij. The system of coordinates for calculation of the dipole-dipole interaction. The direction of the g z component was assumed to be perpendicular to the least-squares plane of the equatorial ligands of each copper atom, while the g x direction dissected the projections of the Cu-O bonds
onto that plane. The direction of g x defined in that way was only 3.6 o away from the Cu-Cu direction. Tensor D dip was calculated from formulas (3) or (4) above and was subsequently diagonalized. The Dipole-Dipole contribution The point-dipole model (formula 3) gave the diagonal tensor components -98, 49, 59, all in units of 10-4 cm -1 in the coordinates defined above. Several equivalent sets of D and E may be obtained from formulas (1) depending on labeling the axes (i.e. which of the components is called D xx etc.). To analyze the dipolar contribution alone it is convenient to consider the largest component as (D dip ) zz. Thus, the point-dipole model (formula 3) gave D dip =-152. The model with delocalization (formula 4), placing ¼ of an electron at the centre of each equatorial Cu-O and Cu-N bond gave D dip =-142. Finally, D dip =-118 was obtained placing 0.3 of an electron at the Cu-N bond centers and 0.2 at the Cu-O bond centers (all data in units of 10-4 cm -1 ). It seems possible to approach the numerical value of the experimental D by using an appropriate delocalization scheme, but the EPR simulations favor positive sign for the experimental D. The exchange contribution From the experimental D=101, E=-6, values of the three diagonal D tensor components are calculated to be 68, -28 and -40, respectively. For simplicity, we average out the smaller components to obtain values 68, -34, -34. The powder EPR spectra only indicate that the distinguished D tensor component is perpendicular to the Z axis defined by the g z direction, thus two sets: D xx =68, D yy =-34, D zz =-34 and D xx =-34, D yy =68, D zz =-34 are equally probable. The calculation of the dipole-dipole contribution (formula 3) gives (D dip ) xx =-98, (D dip ) yy =49, (D dip ) zz =59 in the g system coordinates. Averaging out the smaller components we get (D dip ) xx =- 98, (D dip ) yy =54, (D dip ) zz =54 (the largest and negative dipolar component must lie along the Cu-Cu direction which in the g system coordinates we call X). The exchange-induced tensor components (D ex ) ii are obtained by subtracting (D dip ) ii from the experimental D ii and we obtain either (D ex ) xx = 166, (D ex ) yy = -88, (D ex ) zz = -88 or (D ex ) xx = 64, (D ex ) yy = 14, (D ex ) zz = -88 These numbers should be treated as very rough estimates in view of the uncertainties in calculating the dipolar tensor D dip.